Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model

TL;DR

This paper presents the first theoretical and numerical analysis of quantum ergodicity and localization in conservative systems using the Wigner band random matrix model, revealing detailed eigenfunction and spectral properties.

Contribution

It introduces a novel analysis of energy shell structure, Green function spectra, and eigenfunction localization in a generic conservative quantum system.

Findings

Localized eigenfunctions are narrow and randomly scattered within the energy shell.

Green function spectral density is extended but sparse across the energy shell.

Eigenfunctions can be both localized and ergodic depending on system parameters.

Abstract

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.